# Central Limit Theorem

• Apr 27th 2010, 08:28 PM
Chief65
Central Limit Theorem
We are studying the Central Limit Theorem and I'm not quite sure how to go about this one...

Two types of coins are produced at a factory, a fair coin, and a biased coin that comes up Heads 55% of the time. We have one of the coins but do not know of which type. We will toss it 1,000 times. If it lands Heads 525 or more times, then we say the coin is biased. If it lands Heads less than 525 times, then the coin is fair. If it is equally likely that we have a fair or biased coin, then what is the (approximate) probability that we shall make a false conclusion?

Any help would be appreciated. Thanks
• Apr 29th 2010, 03:46 AM
CaptainBlack
Quote:

Originally Posted by Chief65
We are studying the Central Limit Theorem and I'm not quite sure how to go about this one...

Two types of coins are produced at a factory, a fair coin, and a biased coin that comes up Heads 55% of the time. We have one of the coins but do not know of which type. We will toss it 1,000 times. If it lands Heads 525 or more times, then we say the coin is biased. If it lands Heads less than 525 times, then the coin is fair. If it is equally likely that we have a fair or biased coin, then what is the (approximate) probability that we shall make a false conclusion?

Any help would be appreciated. Thanks

Well as you are to use the CLT you may suppose that the normal approximation for the number of heads is valid, so in one case you have a Normal distribution with a mean of 500 and an SD of ~=15.8 and in the other a normal distribution with a mean of 550 and a SD of ~=15.7.

CB